Question

Write each of the following sets in Roster form:
i) A= set of all factors of 24
ii)B= set of all prime numbers between 50 and 70
iii)C= set of all integers between $-\dfrac{3}{2}$ and $\dfrac{11}{2}$
iv)D= set of all consonants in the English alphabet which precede k
v)E= set of all letters in the word ‘TRIGONOMETRY’
vi)F= set of all months having 30 days

Answer 1

Hint: In this question, we are given a set in the property of the elements of a set and we are asked to describe the same in the roster form. Therefore, we should first understand the roster method of representing a set and then find out all the elements of the set which satisfy the given condition. Thereafter we can use these elements to write the given set in the set builder form.

Complete step-by-step answer:
In this method we have to convert the set from set builder form to Roster form. Therefore, we should first understand the definition of the set roster form which are as follows
In the roster form, all the elements of the set are written explicitly within curly braces with the elements separated by a comma. For example, if a, b, c, d and e are elements of the set A, then it can be represented as
A={a,b,c,d,e}………………………… (1.2)

In this question, we are given the property of elements of a set and we have to represent it in Roster Form. So, the conversion is as follows:
i)We know that the factors of 24 are 1,2,3,4,6,8, 12 and 24 i.e. which leave remainder zero when 24 is divided by them. Therefore, using equation (1.2), the roster form of the set will be \[A=\left\{ 1,2,3,4,6,8,12,24 \right\}\].

ii)We know that the prime numbers between 50 and 70 are 53,59,61 and 67, which have their factors as 1 and themselves. Therefore, using equation (1.2), the roster form of the set will be $B=\left\{ 53,59,61,67 \right\}$.

iii)We know that $-\dfrac{3}{2}$ corresponds to -1.5 and $\dfrac{11}{2}$ corresponds to 5.5. So, the integers between them are -1,0,1,2,3,4 and 5. Therefore, using equation (1.2), the roster form of the set will be $C=\left\{ -1,0,1,2,3,4,5 \right\}$.

iv)We know that all the consonants in the English alphabets preceding k are b,c,d,f,g,h and j. Therefore, using equation (1.2), the roster form of the set will be $D=\left\{ b,c,d,f,g,h,j \right\}$.



v)We know that all the letters in the word ‘TRIGONOMETRY’ are T,R,I,G,O,N,M,E and Y. Therefore, using equation (1.2), the roster form of the set will be $E=\left\{ T,R,I,G,O,N,M,E,Y \right\}$.

vi)We know that the months having 30 days are April, June, September and November. Therefore, using equation (1.2), the roster form of the set will be $F=\left\{April,\text{ }June,\text{ }September,\text{ }November \right\}$.


Note: We should note that in the roster form, each element should be written only once. Therefore, in point (v), only the distinct elements have been written. Also, we should note that the ordering of the elements in the roster form can be changed as it does not make any difference to the representation of the set.